In this paper, based on a direct method for evaluating hypersingular integrals, a heat flux interface integral equation is presented to calculate the hypersingular interface heat fluxes in multi-medium heat transfer analysis by using the interface integral boundary element method (IIBEM). The recently proposed IIBEM has a significant advantage of a single integral equation method for solving multimedium problems, which makes up for the lack of boundary integral equations to solve multi-medium problems. Compared with conventional multi-domain boundary element method (MDBEM), the IIBEM is more efficient in input data preparation, program coding and computational time. However, a big issue encountered is the determination of interface heat fluxes in multi-medium heat transfer analysis through using IIBEM, since the derived flux interface integral equation involves hypersingular integrals on the interface, and no additional information can be utilized to recover the heat fluxes by using the indirect "traction-recovery" methods. In this paper, based on a new efficient direct method for numerical evaluation of high order singular curved boundary integrals, the hypersingularities in flux interface integral equation are precisely evaluated, and based on the successful implementation of flux hypersingular integral equation, the interface heat fluxes are firstly calculated in the multi-medium heat transfer analysis by using IIBEM. Several two- and three-dimensional numerical examples are given to validate the correctness of the presented method. (C) 2019 Elsevier Ltd. All rights reserved.